Geometric modelling and accuracy enhancement of parallel manipulators.
Thesis DisciplineMechanical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The geometric analysis and accuracy enhancement of parallel topology robots is of theoretical interest as well as having potential for application in industrial settings where parallel robots are used for tasks in which positional accuracy is important. This work presents new techniques for modelling of closed loop mechanisms and applies these experimentally in the calibration of a real parallel topology robot: The Delta robot. This work extends the current literature on serial robot calibration into the realm of parallel robots and presents a systematic approach which does not require the model or solution technique to be adjusted for the particular geometry of the robot under investigation. The geometric modelling technique is quite general although in its current implementation it is only capable of modelling mechanisms that have rotary joints. Theory is presented for modelling of prismatic joints and the model can be adapted to handle joints of any type. The model analyses the structure as if it were a tree of bodies, each connected by a rotary or prismatic joint. A method of calculating the derivatives of the body frame positions with respect to the geometric parameters is also given. A defining characteristic of parallel topology mechanisms is that the kinematic chains form closed loops. Finding the joint configuration that has all loops properly closed is a non-linear minimisation problem referred to as the closure problem. This is solved using the Levenberg-Marquardt technique. For analysis of errors in a robot that is already assembled, an experimental calibration procedure is necessary. This procedure compares measured endpoint positions with those predicted by the geometric model and attempts to find a set of parameters that minimises these differences. The calibration procedure that was developed was tested on a number of simulated robots and a working Delta robot, which was designed and built specially for the calibration experiment. The mechanical design of the robot, software and hardware design of the robot controller, and the software implementation of the modelling and calibration procedures are described. It was found that the modelling, identification, and implementation methods worked successfully on the robots examined, but that the implementation process was too slow for use in a practical controller because of the need to perform multiple direct geometric solutions. The computational effort required for the implementation procedure was considerable, but use of a compiled computer language and optimised code would provide significant improvement.